Fifty ping-pong-balls are numbered 1, 2, 3, ..., 49, 50. A ball is chosen at random. What is the probability that the number on the selected ball is a multiple of 5 or 7 or both? Express your answer as a common fraction.
Solution: There are 10 balls whose number is divisible by 5. The balls $7, 14, \ldots,49$ are multiples of 7.  There are 7 of these.  The ball 35 is the unique ball that is a multiple of both 5 and 7.

In total, there are $10+7-1 = 16$ balls whose number is divisible by 5 or 7.  The probability that a randomly selected ball will be one of these 16 is $\frac{16}{50} = \boxed{\frac{8}{25}}$.